Combining assets to obtain a superior balance between risk and return

Combining assets to obtain a superior balance between risk and return

How an investor can combine different assets to obtain a superior balance between risk and return

Order instruction

We aim to improve your understanding of how, in theory, an investor can combine different assets to obtain a superior balance between risk and return, and how traded options (one of the most common forms of derivative) work. You will also apply what you have learned to comparing the relative merits of investment funds.

Hints: Part A

In Part A, Question 1 is designed to help you build up your understanding of Markowitz efficiency and portfolio theory. You will find it useful to look back at Online Unit 3 and Chapter 3.

In your answers to Questions 1c(ii) and 1d, you are recommended to first practise using the Portfolio segment of the Investment Tool by working through the teaching and activities in Online Unit 3. You need to consider data from both the Performance and the Risk/Return tabs in the Portfolio segment, and you are advised to try different combinations of the securities specified before deciding on your answer. You could use diagrams to illustrate your reasoning either by copying and pasting the relevant diagram(s) from the Investment Tool (the Investment Tool guidance instructs you how to do this) or, if you prefer, by making your own copy of the diagram(s) shown in the Investment Tool.

Question 2a requires you to briefly explain the type of option that best fits each objective and how this would work. For Question 2b, you are not expected to give precise calculations, but an answer could be illustrated with actual numbers if you wish. A similar example, for the alternative case of put options, is provided in Activity 4.3 of Online Unit 4.

Question 2c requires you to think about the profile of investors described in the extract (age, goals, life-stage, expertise). You may find it useful to refer back to some of the investment risks considered in Chapter 2 of the module textbook. You do not need to write long answers. Question 2d does not require you to use the extract but instead to use material in the module to provide some explanation about the wider risks of trading options and derivatives.

Hints: Part B

Question 3 requires you to write an essay that draws on the information provided in Table 2, showing that you have thought about what an investor might expect from investment funds. This essay should include definitions of the terms ‘active’ and ‘passive’, as well as comments and definitions of the different performance indicators; it should also describe how these relate to relevant theory, such as the Capital Asset Pricing Model.

Part A  – Question 1   – 1000 Words

a.
Explain what is meant by an efficient frontier in portfolio theory. (4 marks)

b.
Briefly explain what would be the rationale for a tyre manufacturer, in a relatively wet country like the UK, to keep producing tyres that are needed in dry weather. (2 marks)

c.
Gemma has just been given some shares in easyJet. She would initially like to combine these in a portfolio with another share.

i.
If she has only the information in Table 1 available, identify which asset would be sensible to choose and why. (2 marks)

ii.
Using the Investment Tool (Portfolio segment), calculate the optimal proportions of such shares in Gemma’s portfolio to minimise its risk. Report the risk and the expected annualised return of such a portfolio. (5 marks)

d.
Gemma is not happy with this outcome and would like to use one of the shares in Table 1, in combination with easyJet, to construct a portfolio with a much greater expected return (above 20%) but a risk no greater than 5%. Using the Investment Tool (Portfolio segment), identify:

i.
which of the four remaining shares would allow such a combination

ii.
the minimum risk that can be achieved for this portfolio while still reaching an expected annualised return of at least 20%

iii.
the proportion of easyJet shares in this new portfolio. (6 marks)

e.
Briefly explain why Gemma would not adopt a stock-picking strategy, of the type described in 1c and 1d above, if she believed in the semi-strong form of the Efficient Markets Hypothesis? (6 marks)

Table 1: Correlation coefficients between monthly real returns

	BSkyB	Glaxo	Diageo	Rolls-Royce	Tesco
easyJet	0.15	0.12	0.37	0.40	0.22

Question 2

Read the extract below and answer the following questions.

a.
Briefly explain which options could be used by Mark Brisley and Evie Petrikkou to:

i.
protect their portfolio of shares (3 marks)

ii.
increase their income. (3 marks)

b.
The last two paragraphs of the extract give an example of the potential gains and losses that can be made from issuing a call option. Explain how the potential loss per share would increase if the issuer of the call option no longer owned the shares. (7 marks)

c.
Describe two risks of option trading for ‘do-it-yourself investors’: baby boomers such as those described in the extract. (6 marks)

d.
Considering the entire market of derivatives, briefly explain how they could affect systemic risk. (6 marks)

New baby boomer hobby: trading options

After the financial crisis of 2008 hit their stock portfolio hard, Colorado Springs information technology contractor Mark Brisley and his wife Evie Petrikkou were worried. Casting about for a way to make up big losses, the two hit upon a strategy often considered the purview of Wall Street insiders: They could trade options.

Brisley began with the basics, buying and selling ‘puts’ – contracts that convey the right to sell a stock – to earn a little bit extra and protect the family portfolio from another debacle. Initially, he didn’t dabble in ‘calls’ – contracts that convey the right to buy a stock.

Now, five years later, he is a habitual trader who has embraced increasingly arcane options strategies. ‘We treat it almost like a business,’ says Brisley, 51.

Brisley may be the new typical options player – a do-it-yourself investor with a touch of gray. The average options trader now is 53 years old; 28 per cent of all options users are between the ages of 55 and 64, according to the Options Industry Council, a trade group. And those mom-and-pop enthusiasts have pushed trading volume up 16 per cent a year (by number of contracts) for the past decade, according to the Chicago-based OCC, the world’s largest equity derivatives clearing organization

When Fred Tomczyk, chief executive of brokerage firm TD Ameritrade, recently went to an investor education class on options trading, he noticed the crowd around him. ‘It was all people who look like me,’ Tomczyk, 58, told Reuters in a recent interview. ‘It was older people who are about to retire or just retired.’

Jared Levy, author of ‘Your Options Handbook’ and managing partner at Belpointe Alternative Investments in Greenwich, Connecticut, says it is no surprise that baby boomers are driving the options train. ‘A lot of the increasing volume has been coming from boomers with high net worth who have gained the ability to trade from home.’

But retirees should think twice before trading in their tennis rackets or bridge games for an options-trading hobby. Options are complex derivative instruments that may protect your portfolio and let you squeeze in some extra earnings – or cause you to lose your shirt and your pants along with your stock holdings.

Most share options allow traders in effect to place bets on the movement of share prices, and individual investors are notoriously bad about timing those bets in the first place. In fact, a recent analysis of more than 200,000 investors done for Reuters by online financial planning platform SigFig revealed that those who did not trade options thumped those who did. Investors who stayed away from options racked up 13.2 per cent in portfolio gains for the year ended June 25, while those who embraced the options trade lagged by 6 percentage points, with returns of 7.3 per cent.

In their basic form, options contracts are known as puts and calls. The buyer of a put has a right to sell the asset (like 100 shares of a stock or exchange-traded fund) at an agreed-on price. That could provide downside protection if the asset plummets in value. A call conveys the right to buy shares at an agreed-on price.

Say, for example, you own 100 shares of a company trading at $50 a share. You could sell a 90-day call at a $60-per-share strike price, for $200. If the stock goes down, you’ll keep the $200 and the call will expire. If the stock goes up to $58, you’ll keep the shares, the $200 and the $800 gain (on 100 shares). Again, the call will expire.

If the stock goes up to $75, you’ll keep the $200 and the $10 per-share gain between $50 and $60. But you’ll lose the extra $15 per share in gains because you’ll have to sell the stock at $60 a share – it will have been ‘called’.

Word limit Part B: 1000 words

Part b -Question 3

Compare the performance, risk and charges for the three funds reported in Table 2. To what extent might this data provide useful evidence to guide an investor in choosing between an active or passive approach to investing?

 Table 2: Fund performance data

Fund	Type of fund	Annualised returns %			3-year data					OC (% pa)
		1 year	3 year	5 year	Volatility	Alpha	Beta	Sharpe ratio	R-squared
Baillie Gifford UK Equity Alpha	Active	28.79	14.38	18.92	14.42	2.05	1.07	0.72	0.91	1.55
F&C UK Alpha	Active	10.96	2.14	12.83	13.44	–6.79	0.99	0.08	0.92	1.72
HSBC FTSE All-Share Tracker	Passive	23.22	10.52	15.29	13.19	–0.67	1.03	0.46	0.92	0.17
FTSE All-Share Index		22.20	10.63	16.94

Source: www.trustnet.com and www.morningstar.co.uk (Accessed 29 October 2013)

Notes: OC stands for ongoing charges. HSBC FTSE All-Share Tracker tracks the FTSE All-Share Index.

Annualised total returns are calculated per annum on the bid price of 29 October over the respective period of 1 year, 3 years and 5 years (with net income reinvested).

SAMPLE ANSWER

Combining assets to obtain a superior balance between risk and return

Introduction

Correlation coefficient is applied when analyzing different types of stocks and asset behavior. Asset correlation in personal investing guards against exposure to excessive risks. It however doesn’t account for the reasons, causes or effect of the risks. (Markowitz 2009)

1a. Efficient frontier in the portfolio theory

It’s a theory in modern portfolio management that was initiated by Markowitz and it involves various combination of assets or portfolio in a way that brings out the best level of expected returns in an efficient way considering its level of risks. The standard deviation of the asset returns is plotted against the portfolios expected return which is obtained against the tangent of a risk free rate. The part of the hyperbola that represents the opportunity with the highest amount of expected return for a particular level of risk is known as the efficient frontier. (Elton & Gruber 2011)

1b. The rationale would be that the tyre manufacturer basically produces enough tyre for the UK market and also enough for export to other countries that would have a different kind of weather some may be dry. UK tyre manufacturer would have to satisfy even the markets that require the tyres that are needed in dry weather.

1c. i) The best assets would be Rolls-Royce and BSkyB stock. The stock represents very high returns but the risks are also high. The relationship that exists between the above stocks and the gains in the FTSE are very strong and positive relationship with the portfolio. For example a positive relationship shows a positive gain in the FTSE and the portfolios while a negative correlation coefficient shows that could actually lose some portfolio value as the FTSE gain gains value.

1c. ii) investors prefer investments with higher returns as well as investments with low risks. The best option is to select the most suitable and profitable option from the efficient frontier. The best way to point out the best option is by evaluating the indifference curves which represent the preference of the investors on different combination of risks and returns.

Optimal Performance calculations of EasyJet

	Easyjet	Glaxo	Port	BSkyB	Port	Diageo	Port
Expected Val mon %	2.32	0.30	1.31	1.22	1.77	1.07	1.70
Expected Ret (ann %)	31.72	3.60	16.89	15.72	23.48	13.60	22.35
Variance	71.50	22.94	26.04	45.54	33.43	16.01	28.12
STD %	8.46	4.79	5.10	6.75	5.78	4.00	5.30
5 yrs Beta	0.86	0.45	0.65	0.49	0.67	0.52	0.69
5 yr Alpha %	27.20	0.42	13.04	12.42	19.57	10.20	18.39
5 yr Sharpe ratio	3.55	0.40	2.98	2.08	3.77	2.98	3.90
5 yr total return	222.44	11.51	102.10	81.98	160.65	80.28	152.56
	HSBC	port	Roll Ro	Port	Tesco	Port
Expected Val mon %	0.17	1.25	1.95	2.14	-0.18	1.07
Expected Ret (ann %)	2.10	16.05	26.06	28.86	-2.11	13.66
Variance	37.17	31.31	36.96	37.50	37.31	32.78
STD %	6.10	5.60	6.08	6.12	6.11	5.73
5 yrs Beta	0.26	0.56	0.91	0.88	0.73	0.79
5 yr Alpha %	-0.43	12.52	21.38	24.26	-6.22	9.34
5 yr Sharpe ratio	0.07	2.57	4.01	4.44	-0.06	2.09
5 yr total return	-0.78	92.07	186.51	219.17	-19.70	72.23

The minimum risk is 5%

1d. i)  Diageo

	Expected returns	Risks
Tesco	14%	6%
Rolls Royce	29%	6%
HSBC	15%	5.50%
Glaxo	17%	5%
Easy jet	31.72%	8.46%
Diageo	22.35%	5.30%
BSkyB	23%	5.78%

1d. ii) 5.3%

1d. iii) The proportion of Easyjet shares would be 50%.

1e. The lowest standard deviation and the average return of the portfolio and the capital allocation line gives the Sharpe ratio. The optimal portfolio balance is usually where the line’s slope is highest.

2a. i)  The major challenge in the management of investment is basically the choosing of a convenient and appropriate investment while also designing a particular unit that will meet the expectation and the objective of the investor while also considering his constraints. These constraints could be the liquidity, need for regular monthly or periodical income, age, the risk tolerance or even the tax liability. Investments can be classified broadly as financial or real investments while financial investment can be further classified as fixed income or variable income investments.

To protect their shares portfolio, Mr. Mark Brisley and EviePetrikkou should sell a call that’s covered. For example, if they owned 100 or more shares that they intended to sell as stock (writes) that’s a call option. The buyer of the option would pay a premium so as to gain the right to buy the 100 shares at an agreed price known as the strike price for a certain limited time that’s until the options expire. If the stock’s value appreciates the option owner gains otherwise all the gains would have all ended up with the stockholder. The cash ensures protection from the stock price devaluation. They can also protect their shares portfolio by buying puts. For example during the 2008 economic crisis, the value of puts would generally have increased as the stock’s value deteriorated. The put owners have a right to sell their shares at the agreed strike price. The main advantage of buying puts is that the losses are mostly limited. The owner is allowed to pick a strike price that can match the risk tolerance and the minimum selling price is also guaranteed. The value of the portfolio cannot be allowed to fall beyond a certain amount. The other alternative is to replace all the stocks with options.

2a. ii) They can increase their chances of getting more income by taking options with a longer period of time that the option can be exercised.

2b) The potential loss per share would increase if the value of the shares reduces to 45 per share or less. After buying the options for 50 per share, the potential loss would increase to 5 per share which will culminate to a loss 500 for the 100 shares excluding the 200 premium.

2c) The risks in the extract can be analyzed from two approaches, the sellers and the buyers. When a trader purchases an asset that has a three months expiration and within that period the potential stock remains at a price that is lower than its original purchase price, then the risk of getting losses is inevitable.

The sellers also incur losses as there are some options that have unlimited risks or possibility of ending up in losses which largely depend on the movement of the potential stock. There are instances where the sellers are under obligation to sell even when the trading is not profitable.

Risks are inherent to any form of trading as the higher the risk the higher the profits.

2d)  Derivatives have contributed largely to the need of increased risk management procedures. Derivatives have to led to the growth of the financial economy which had been preceded by the production economy in the late 1960,s and early years of 1970’s. (Ciner 2006)

Derivatives can affect systematic risks as its nature and implication go beyond the realms of the entire financial economy, social and also political framework of most economies. (Dodd 2005)  This is possible as derivatives do not affect the underlying asset but only the price change of the asset which predisposes the assets to wide range of systematic risks. (Williams 2010)  With increased innovations derivatives have evolved into new forms which have created cross-linkages in different asset valuation and price changes through different forms of automated digital platforms like swaps. (Blackburn 2008)  Swaps provide the means and capacity to exchange one asset risk which is in a different class to another without actually gaining ownership of any asset with the investors. Such innovation has increased systematic risks that are associated with different forms of derivatives and has contributed to the interdependency of several different assets and their relative price changes. (Zeyu, Podobnik, Feng and Baowen 2012)  Instability in only one class of a certain assets can cause a very widespread effect on the systematic stability several other related assets hence create a complex manifestation of associated risk in a financial economy. (Brownlees, Engle 2010)

3b)  Alpha is also known as the Jensen index and it measures the risk adjusted return of an equity security while beta measures the volatility of the security as compared to its benchmark index. It basically indicates the securities or the stocks ability to gain value and it’s based on the company’s rate of earnings growth. Volatility measures the riskiness of a particular stock compared to the market. R-squared determines the exact proportion of a stock or security’s return. The F&C  r-squared of 0.92 indicates that 92% of the returns of the security are basically due to the gains in the market while 8% is due to other factors related to the security. Sharpe ratio compares the overall relationship of risks and related rewards while exploring different investment strategies. Its Sharpe ratio is 0.08 or 8% and it’s the most risky security among the three as its ratio is the lowest.  A higher ratio indicates a less risky investment. The F & C beta of 0.99 shows that the market has similar risks as the security while the r squared of 0.92 indicates that the bench mark index is almost wholly determined by the portfolio’s performance. It’s very high and it’s also referred to as the coefficient of determination. The volatility for F & C shows that its lower than 50% hence its acceptable as the beta is also close to 1.

The Baillie  r-squared of 0.91 indicates that 91% of the returns of the security are basically due to the gains in the market while 8% is due to other factors related to the security. Sharpe ratio compares the overall relationship of risks and related rewards while exploring different investment strategies. Its Sharpe ratio is 0.72 or 72% which is the best among all the portfolio and it’s the safest to invest in as it’s less risky than all the rest of the securities. A higher ratio indicates a less risky investment. The Baillie beta of 1.07 shows that the market has similar risks as the security while the r squared of 0.91 indicates that the bench mark index is almost wholly determined by the portfolio’s performance. The volatility for Baillie shows that it’s lower than 50% hence it’s acceptable as the beta is also close to 1. (Elton & Gruber 2011)

The HSBC  r-squared of 0.92 indicates that 92% of the returns of the security are basically due to the gains in the market while 8% is due to other factors related to the security. Sharpe ratio compares the overall relationship of risks and related rewards while exploring different investment strategies. The 0.46 or 46% shape ratio indicates that its return is risky. A higher ratio indicates a less risky investment. The HSBC beta of 1.03 shows that the market has similar risks as the security while the r squared of 0.92 indicates that the bench mark index is almost wholly determined by the portfolio’s performance. The volatility for Baillie shows that it’s lower than 50% hence it’s acceptable as the beta is also close to 1.

Reference

Brownlees, C.T., Engle, R.F., 2010. Volatility, correlation and tails for systemic risk measurement,

Blackburn, R., 2008, The Subprime Crisis, New Left Review, 50 Mar- Apr 2008.

Ciner, C., 2006, Hedging and Speculation in Derivatives Markets: the Case of Energy Future Contracts, Applied Financial Economics letters, 2, 189-192

Dodd, R., 2005, Derivatives Markets: Sources of Vulnerability in US Financial markets, In Gerald A. Epstein (Ed) Financialization and the World Economy, Edward Elgar: Cheltenham

Elton, E.J. & Gruber, M.J., 2011, Investments and Portfolio Performance. World Scientific. pp. 382–383.

Gray, D. F. and Andreas A. J., 2011, “Modeling Systemic and Sovereign Risk,” in: Berd, Arthur (ed.) Lessons from the Financial Crisis (London: RISK Books), pp. 143–85.

Markowitz, H.M., 2009, Harry Markowitz: Selected Works. World Scientific-Nobel Laureate Series: Vol. 1. Hackensack, New Jersey: World Scientific. p. 716

Sullivan, A. & Sheffrin, S.M., 2003, Economics: Principles in action. Upper Saddle River, New Jersey

Williams, M.T., 2010, “Uncontrolled Risk: The Lessons of Lehman Brothers and How Systemic Risk Can Still Bring Down the World Financial System”. Mcgraw-Hill

Zeyu, Z., Podobnik, B., Feng, L. and Baowen L., 2012, “Changes in Cross-Correlations as an Indicator for Systemic Risk” (Scientific Reports 2: 888 (2012))

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